Does seem like AJ, 77 or JJ, but still...I think he has a bunch of other stuff in his calling range and if we fold here...did we 3bet just to get him to fold preflop? If he 4bets do we fold preflop? He seems to call a lot preflop, so we shouldnt fold on A-high flops, imo. If he 4bets a lot it might seem more like a set or AJ.
How many hands? Cause f3bet is pretty low...if its over a good sample I'm def not folding here. Either calling and hoping he keeps bluffing, or shipping and hoping he has a flush draw, or AQ, but I don't see why he'd raise AQ on the flop...or a set actually, why not let you bet again on the turn. I don't think he has to protect from the flush draw. And I think your cbet seems weak-ish too. I know 1/2 pot is pretty common in 3bet pots but I think its often used by people who bluff 3bet often and then cbet as a bluff often to balance.
Anyways, I'm a fish and I just find the situation interesting and would like some more thoughts